We investigate the numerical solution of large scale linear and quadratic matrix equations. A special focus here lies on the solution of large scale continuous time Sylvester, Lyapunov and Riccati equations as appearing in model reduction and linear quadratic regulator problems for semidisretized PDEs. The methods employed are based on the low rank alternating directions implicit iteration and the outcome directly supports the development of our software library and Matlab toolbox M.E.S.S.